Shifting a Housecleaning Tax. Consider a city where poor people clean the houses of rich people. Initially, housecleaning firms charge their customers $10 per hour, keep $1 per hour for administrative costs, and pay their workers $9 per hour. Like many luxury goods, the demand for housecleaning service is very elastic. Housecleaning workers are not very responsive to changes in the wage.

a. Use supply and demand curves to show the initial equilibrium in the market for cleaning services (price = $10 per hour; quantity = 1,000 hours of cleaning per week), and label the equilibrium as point a.

b. Suppose the city imposes a tax of $3 per hour on cleaning services, and one-third of the tax is shifted forward to consumers. Use your graph to show the effects of the tax on the housecleaning market. Label the new equilibrium as point b. What is the new price?

c. Is it reasonable that only one-third of the tax is shifted forward? Explain

d. Suppose that firms continue to keep $1 per hour for administrative costs. Predict the new wage.

e. Who bears the bulk of the housecleaning tax, wealthy households or poor ones?